Robust Regulation of Markovian Jump Linear Systems Subject to State Time Delay and Uncertain Transition Probabilities

ABSTRACT Controlling dynamic systems free from abrupt changes, dependent only on current states and completely known parametric matrices, is often impractical. Hence, it is essential to develop control strategies that regulate the state regardless of unknown variations in the system. This paper addresses the robust recursive regulator problem regarding discrete‐time Markovian jump linear systems subject to delayed state and norm‐bounded uncertain data. We assume the uncertainties impact the state‐space parameters and the transition probability matrix. The time delay is random within a known interval, and the maximum variation rate of the delay is considered. Employing the augmented system approach, we represent the time delay by a known Markov chain, resulting in a delay‐free Markovian system. We formulate a min‐max optimization problem based on the penalization of least squares and devise a recursive algorithm to achieve robust state feedback gains. We further show that coupled Riccati equations can achieve convergence and stability conditions. Comparative examples show the effectiveness of the proposed approach.